{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discretisation\n",
    "\n",
    "Discretisation is the process of transforming continuous variables into discrete variables by creating a set of contiguous intervals that spans the range of the variable's values.\n",
    "\n",
    "### Discretisation helps handle outliers and highly skewed variables\n",
    "\n",
    "Discretisation helps handle outliers by placing these values into the lower or higher intervals together with the remaining inlier values of the distribution. Thus, these outlier observations no longer differ from the rest of the values at the tails of the distribution, as they are now all together in the same interval / bucket. In addition, by creating appropriate bins or intervals, discretisation can help spread the values of a skewed variable across a set of bins with equal number of observations.\n",
    "\n",
    "\n",
    "### Discretisation approaches\n",
    "\n",
    "There are several approaches to transform continuous variables into discrete ones. This process is also known as **binning**, with each bin being each  interval. Discretisation methods fall into 2 categories: **supervised and unsupervised**. Unsupervised methods do not use any information, other than the variable distribution, to create the contiguous bins in which the values will be placed. Supervised methods typically use target information in order to create the bins or intervals.\n",
    "\n",
    "####  Unsupervised discretisation methods\n",
    "\n",
    "- Equal width binning\n",
    "- Equal frequency binning\n",
    "\n",
    "\n",
    "#### Supervised discretisation methods\n",
    "\n",
    "- Discretisation using decision trees\n",
    "\n",
    "\n",
    "In this lecture, I will describe **equal width discretisation**.\n",
    "\n",
    "\n",
    "## Equal width discretisation\n",
    "\n",
    "Equal width binning divides the scope of possible values into N bins of the same width.The width is determined by the range of values in the variable and the number of bins we wish to use to divide the variable.\n",
    "\n",
    "width = (max value - min value) / N\n",
    "\n",
    "For example if the values of the variable vary between 0 and 100, we create 5 bins like this: width = (100-0) / 5 = 20. The bins thus are 0-20, 20-40, 40-60, 80-100. The first and final bins (0-20 and 80-100) can be expanded to accommodate outliers (that is, values under 0 or greater than 100 would be placed in those bins as well).\n",
    "\n",
    "There is no rule of thumb to define N. Typically, we would not want more than 10.\n",
    "\n",
    "I will demonstrate how to perform equal width binning using the Titanic dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Titanic dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "% matplotlib inline\n",
    "\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>7.2500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>38.0</td>\n",
       "      <td>71.2833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>26.0</td>\n",
       "      <td>7.9250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>35.0</td>\n",
       "      <td>53.1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>8.0500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Survived   Age     Fare\n",
       "0         0  22.0   7.2500\n",
       "1         1  38.0  71.2833\n",
       "2         1  26.0   7.9250\n",
       "3         1  35.0  53.1000\n",
       "4         0  35.0   8.0500"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load the numerical variables of the Titanic Dataset\n",
    "\n",
    "data = pd.read_csv('titanic.csv', usecols = ['Age', 'Fare', 'Survived'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fill missing data with random sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((623, 3), (268, 3))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's separate into train and test set\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(data[['Age', 'Fare', 'Survived']], data.Survived, test_size=0.3,\n",
    "                                                    random_state=0)\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variable Age contains missing data, that I will fill by extracting a random sample of the variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def impute_na(data, variable):\n",
    "    df = data.copy()\n",
    "    \n",
    "    # random sampling\n",
    "    df[variable+'_random'] = df[variable]\n",
    "    \n",
    "    # extract the random sample to fill the na\n",
    "    random_sample = X_train[variable].dropna().sample(df[variable].isnull().sum(), random_state=0)\n",
    "    \n",
    "    # pandas needs to have the same index in order to merge datasets\n",
    "    random_sample.index = df[df[variable].isnull()].index\n",
    "    df.loc[df[variable].isnull(), variable+'_random'] = random_sample\n",
    "    \n",
    "    return df[variable+'_random']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# replace NA in both  train and test sets\n",
    "\n",
    "X_train['Age'] = impute_na(data, 'Age')\n",
    "X_test['Age'] = impute_na(data, 'Age')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Age\n",
    "### Original distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x18edeeb0f0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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pXqqruaC72c7XXFObNtTabvnfZBd1NVuTXLOzswcyc3rQeo2KPiJ+DNgHfC4zf3+VxyeB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\nPtQLY00AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18ed4d5390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's remind ourselves of the distribution of Age\n",
    "data.Age.hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**How does survival correlate with Age?**\n",
    "\n",
    "We can determine the relation between survival and Age by plotting the mean survival per Age. In this case, I will calculate the Survival rate per each year of Age. See below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x18ef398978>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A36zZmIrxMrpBo0U/akCmmMLnJBusrGlQhkEhKlIHGsRwrc4rDRvFHJ8UdY1A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\nFksi/wd7GFwzqxLsNgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18edeeb550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "fig = data.groupby(['Age'])['Survived'].mean().plot()\n",
    "fig.set_title('Normal relationship between variable and target')\n",
    "fig.set_ylabel('Survived')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By looking at the plot, we get an intuition that younger people (children) were more likely to survive (see higher survival rates at ages below 10 and 10-15). However, it looks like children of 10 years of age, had a very low survival chance. This does not make a lot of sense and most likely indicates that our 10 year old sample is not big enough and then the survival rate is underestimated. Let's see below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x18ef398fd0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZIzENQ2sKGo2CuJpCjoh+iohMIjKI6KcA5Fp5Y5po+NQ1M1QbEKiE5lrzFIDq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18ef4342e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "fig = data.groupby(['Age'])['Survived'].count().plot()\n",
    "fig.set_title('Number of people per year age bin')\n",
    "fig.set_ylabel('Survived')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we suspected, there were very few children at the age of 10 on the Titanic. If none of them or only half of the 10 year old children survived, we would be led to think that being 10 years old decreased your chances of survival, when in reality, there were only 2 children of the age that were not lucky enough  to survive, therefore leading to underestimation of survival rate.\n",
    "\n",
    "By grouping Age into bins, we can get a better view of the survival rate depending on the Age of the passenger. Let's see below.\n",
    "\n",
    "### Discretisation with range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "79.329999999999998"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's capture the range of the variable age to begin with\n",
    "\n",
    "Age_range = X_train.Age.max() - X_train.Age.min()\n",
    "Age_range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.9329999999999998"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's divide the range into 10 equal width bins\n",
    "\n",
    "Age_range/10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The range or width of our intervals will be 8 years."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 80, 8)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# not let's capture the lower and upper boundaries\n",
    "\n",
    "min_value = int(np.floor(X_train.Age.min()))\n",
    "max_value = int(np.ceil(X_train.Age.max()))\n",
    "\n",
    "# let's round the bin width\n",
    "inter_value = int(np.round(Age_range/10))\n",
    "\n",
    "min_value, max_value, inter_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's capture the interval limits, so we can pass them to the pandas cut function to generate\n",
    "# the bins\n",
    "\n",
    "intervals = [i for i in range(min_value, max_value+inter_value, inter_value)]\n",
    "intervals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Bin_1',\n",
       " 'Bin_2',\n",
       " 'Bin_3',\n",
       " 'Bin_4',\n",
       " 'Bin_5',\n",
       " 'Bin_6',\n",
       " 'Bin_7',\n",
       " 'Bin_8',\n",
       " 'Bin_9',\n",
       " 'Bin_10']"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's make labels to label the different bins\n",
    "labels = ['Bin_'+str(i) for i in range(1,len(intervals))]\n",
    "labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Age_disc_labels</th>\n",
       "      <th>Age_disc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>857</th>\n",
       "      <td>51.0</td>\n",
       "      <td>26.5500</td>\n",
       "      <td>1</td>\n",
       "      <td>Bin_7</td>\n",
       "      <td>(48.0, 56.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>49.0</td>\n",
       "      <td>76.7292</td>\n",
       "      <td>1</td>\n",
       "      <td>Bin_7</td>\n",
       "      <td>(48.0, 56.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>386</th>\n",
       "      <td>1.0</td>\n",
       "      <td>46.9000</td>\n",
       "      <td>0</td>\n",
       "      <td>Bin_1</td>\n",
       "      <td>(-0.001, 8.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124</th>\n",
       "      <td>54.0</td>\n",
       "      <td>77.2875</td>\n",
       "      <td>0</td>\n",
       "      <td>Bin_7</td>\n",
       "      <td>(48.0, 56.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>578</th>\n",
       "      <td>14.5</td>\n",
       "      <td>14.4583</td>\n",
       "      <td>0</td>\n",
       "      <td>Bin_2</td>\n",
       "      <td>(8.0, 16.0]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Age     Fare  Survived Age_disc_labels       Age_disc\n",
       "857  51.0  26.5500         1           Bin_7   (48.0, 56.0]\n",
       "52   49.0  76.7292         1           Bin_7   (48.0, 56.0]\n",
       "386   1.0  46.9000         0           Bin_1  (-0.001, 8.0]\n",
       "124  54.0  77.2875         0           Bin_7   (48.0, 56.0]\n",
       "578  14.5  14.4583         0           Bin_2    (8.0, 16.0]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create binned age\n",
    "\n",
    "# create one column with labels\n",
    "X_train['Age_disc_labels'] = pd.cut(x = X_train.Age, bins=intervals, labels=labels, include_lowest=True)\n",
    "\n",
    "# and one with bin boundaries\n",
    "X_train['Age_disc'] = pd.cut(x = X_train.Age, bins=intervals, include_lowest=True)\n",
    "\n",
    "X_train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see in the above output how by discretising using equal width, we placed each Age observation within one interval /bin. For example, age 51 was placed in the 48-56 interval, whereas age 14.5 was placed into the 8-16 interval.\n",
    "\n",
    "Because we discretised the variable using equal width intervals instead of equal frequency, there won't necessarily be the same amount of passengers in each of the intervals. See below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Age_disc\n",
       "(-0.001, 8.0]     49\n",
       "(8.0, 16.0]       36\n",
       "(16.0, 24.0]     147\n",
       "(24.0, 32.0]     146\n",
       "(32.0, 40.0]     112\n",
       "(40.0, 48.0]      68\n",
       "(48.0, 56.0]      37\n",
       "(56.0, 64.0]      19\n",
       "(64.0, 72.0]       7\n",
       "(72.0, 80.0]       2\n",
       "Name: Age, dtype: int64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.groupby('Age_disc')['Age'].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x18ef4cc978>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hlS0iaQcA2w9O5wxNydGEDE3J0YQMTckxiAxD+2WspMMlnSlpSbmdKemIaZhhV0kXSRoD\nrgGulbS2rBudLhmakqMJGZqSowkZmpJj4BlsD90NOI3qrNv5wB+V2/yy7lPTJUPJcRXwBmBGx7oZ\nJcvV0yVDU3I0IUNTcjQhQ1NyDDrDUHbdSLrNE3w7LUnAbbbnTIcMpb3bJ2trfdvalqEpOZqQoSk5\nmpChKTkGnWFYv4z9laT9bV83bv3+wK+mUQaA5ZLOABbx5GQvuwALgDpGNDQlQ1NyNCFDU3I0IUNT\ncgw0w7Ae0e8LnAk8g2r2KqhetJ8DJ9pePh0ylBxbAMdTDfdcN4vXKuCfgc/Z/vV0yNCUHE3I0JQc\nTcjQlByDzjCUhX4dSc/myRftPttrpmOGiIj1GdpRNwC219heXm4DKbBNyDAZSa9KhkoTcjQhAzQj\nRxMyQDNy1JFhqAv9RCStSIYn7D/oADQjAzQjRxMyQDNyNCEDNCNH3zMMdddNRERs2LCOunkaSbNs\nD2xWd0nbAnOAn9p+aFA5SpaP2f5QzW1uC4zY/sm49X9o+0c15ngmcAQd35sAl9p+uMYMLwHut32r\npIOBg4BbbF9SY4ZdgbW2f1WG/L4F2Be4Gfis7cfqyjIuV+37Zml34PvnIPfNoTyil3QkcAbVC/V2\n4HxgK2BLYIHtpTVkOB94p+2fSToc+CxwG1Wxf6/tL/U7Q8kx/iqaAt4MnAdg+6QaMhxDdQLZWmBz\n4C3rhp1KWmF7335nKG39CfAR4DKqfQNgZ+DlwN/aPq+GDKcBB1AdRF0KHAZ8C3gpcL3t9/U7Q8lx\nE3CA7UclnQrsAXwNOBTA9nE1ZBj4vllyDHz/HPi+WcdZYb2+ATcAe1IdKT0AHFjW7wmsqCnDjR3L\n/waMluVZwA9rfC3upXqj+xOqMbkLgLF1yzX+PWaX5QOAHwOvKfevr/G1uBXYboL121OdxFZHhpVU\nBW1r4CFg67J+c+CmGl+LmzuWlwObddyvZf9swr5Zcgx8/xz0vjmsX8Y+bvsW21cBj9q+GsD2LdT3\nBfNm5eMgwOPAPSXDz6i3S2wv4GdUHwkvd3VFzUdsL/IGrq7ZQzNsrwawfS3wx8CHJZ0E1PmRUZO0\n93jZVge7+h/8+Lr7HRnq/P92r6RDy/JdVOd4IOlZNWZowr4Jzdg/B7pvDmsf/cOS/hzYFnhI0ruA\nxcDLgF/WlOFvgSskfQb4AfAlSUuodqJv15QB248A75S0H3CBpEuofzTVI5L2cOn/tL1a0iFUXQV7\n15jjZGCFpMt48uzDXak+Hn+0pgyXSPpXqq7Es4HFkq6m6rq5sqYMAH8KnCfpb6hO4rtB0g3AdsC7\n6wjQkH0TmrF/DnTfHNY++l2oJvR4nKrgHkt11tndVP3jt9SU4znAnwHPpXrTXAV8zfaldbQ/QR4B\nfwkcZPtNNbb7IqpPVrePW785cIztC2rMsj1wOE//wqu2L8glHUR1ZH+1pD2A11B94rvY9uPrf3bP\ns+zJU/fP6+rOUHIMZN8sbTdi/1R1eeJXMIB9cygLfcTGkrSv7YGe19CEDE3QpJFpTVDnSMFh7aNv\nNEkbmmKwl23touqa1v8q6UPlKGXdtq/VlOH5kr4l6RJJe0g6V9LDkq4tR5S1kLTv+BuwRNI+ZXkQ\nGfarO0PJcVzH8k6Slkp6SNK/SerrHK0d7Z4vaVZZPhy4CTiVqhvp9XVkKG0/KOlsSYeVTxa1k3Sk\npDslfb/sCyuBayStknRY39vPEX3vSbrH9q41tXU58GXgaqruq/2A/2n7AUnXewPzVPYow5XAJ4Bt\ngFOADwBfBF5FNQS17ztyyfE41evQeYGoA8s62z50wie2LEPJ8cSwQUmLge9QfWcwD3hbHX8TSTfa\nfmFZ/jfgf9u+qxT/pbZf1O8Mpe1bgU9TdfGOAhcDF64bxFFThhtK+9sB3wCOKl17ewIXuN9DPOsY\nWtTGG/CLSW6PAI/VmOOGcfffRDXEbw/qG2p6fcfyHeO21ZKhtPVa4HvAkR3r7qx5vxh4hvGvO+OG\nU1LfkMKVwLZl+fs8dYjnygG9FrsC7wdWAD8FPjaADPeO23ZDv9tvVdeNpHmSXlxTcw8Dc2xvO+72\nDGB1TRkANpe01bo7ts8H3kF1ss7smjLM6Fj+5LhtW9SUAdtfBo4CXiHpS6rODq31I2sTMhQ7Szpd\n0qeBWZ1delRj+uuwbmTacTw5Mm2BpHOpcWQaHcMXbd9j++OujqBfyVM/efXTw5L+XNL7KCMFS5fa\nAmoYKTiswysn82LghZJm2j6yz22dB+wG3D/Btn/qc9udzqb6d39v3Qrb3yl9oB+vKcNnJG1j+5e2\nz1i3soxK+k5NGQCw/UvgXZL2oZrkYZs6229KBqDzDNxlJcNDqi6rvaSOALYXq7rAX+fItAOpuk3q\nHJl2xST5fkz1ZlSHBTw5UvAVVN04l1KNFPyzfjeePvporfLF2zNs/2I6Z4hoVdcNgKSXDzpDNIMr\nAy2wTcgQ0boj+jpHvEREDIOh7KNXdamBCTcBdV7LIyKi8Yay0AP/g2oY4fhvq0V1dbppT9I8YI3t\na6ZzhqbkaEKGpuRoQoam5Kgrw7AW+quprl3xvfEbyskRAyNp3XV2PmP7HwcYpc4RSE3O0JQcTcjQ\nlBxNyNCUHLVkaF0ffROouhTsga5xRqGIiMkMfaEvV4TD9oPTNYOaMX3ewDM0JUcTMjQlRxMyNCXH\nIDMM5fBKSbuWC3mNAdcA10paW9aNTpcMJcefUJ3OfQjVrEZbU10Tf3nZNi0yNCVHEzI0JUcTMjQl\nx8Az1HGdh17fgKuAN1DNHLNu3QxgPnD1dMlQ2mzC9HkDz9CUHE3I0JQcTcjQlByDzjCUR/TALNtf\ntP3bdSts/9b2RdQ3vLIJGaAZ0+c1IUNTcjQhQ1NyNCFDU3JkKsEpWC7pDKrriKyblmsXqutJXD+N\nMkAzps9rQoam5GhChqbkaEKGpuTIVIKbStIWVNden8dTv9hYAnzOdt+vSDdJhlXAP9eVoSNLE6bP\nG3iGpuRoQoam5GhChqbkGGSGoSz0ERGx8Ya1jx5Jh0s6U9KScjtT0hGDzgUg6VWDzgAg6axkqDQh\nRxMyQDNyNCEDNCNHHRmGso9e0mlU17c+j6q7BGBn4CRJR9p+x8DCVfanmi5s0P7foAPQjAzQjBxN\nyADNyNGEDNCMHH3PMJRdN5Jus/20CY7Ltb9vsz1nALEiIhppWLtufiVp/wnW7w/8qq4Qkl4i6Xll\n+WBJ75V0VF3tl3bfpmqyZSQ9R9KVkh6WdI2kF9aZZVyu2wbQ5gxV07V9VNLB47Z9uKYMM0uGb0v6\nUbl9S9Jf6KnT+fU7xx9I+rykv5O0jaTPSrpJ1fSGozVlaOS+WfLUun8Oet8c1iP6fYEzgWfwZNfN\nLsDPgRNtL68hw2lUV8qcSTUl2GHAt4CXUk2+/L71PL2XOVba3rssXwKcbfurkg4BTrZ98Hp/QW8y\nPMKTY4TXjQneGniUau6NbfudoeQ4u7R7LfBm4Hu23122rXA1T2i/M1xINZ/wIp7arbgA2MH2G/qd\noeS4ErgQeCbVlV7PARZTTWP3RtuH1pBh4PtmaXvg++fA9826zk7r09lmzwb2K7dn19z2SqqdZmvg\nIWDrsn5z4KYac9zasXzduG0/qinD6VTfl+zYse7OAewPP+pYngmcBXwF2JLqzbeODJOe5bi+bX3I\ncX3H8j2TbetzhoHvm6Wtge+fg943h7XrBgDba2wvL7c19TdvU53ZBk8eMTxOvV1iF0s6V9IfAF+V\n9E5Ju0l6K3BPHQFsnwR8CrhQ0kmSNmPiswD7bYuOTI/ZPgG4AfgX6pug+0FJry+vAQCSNpP0BqoD\ngro8Lum5pYtza0lzS5bnUF2qow4D3zehMfvnYPfNOt/VanrnXFFTO6cC/wpcB3yC6kSpvwIuA/5v\nzf/mt1BdWO1nwCPAzcDHgGfWnGMz4KTyuvz7AP725wNHTLD+T4H/qinDKPBFYAy4rdzGyrrda3wt\nDqO6vsotwB8BXwbuANYC82rM0Yh9s2QZ2P456H1zKPvom0LSQVRH9ldL2gN4DdWRysW2H1//s9tL\n0mxgH9vfHHSWQVI1LwG2Hxh0FoDyxehD7rg+03Q0HffPoe66gepa8CrXg6+5Xdm+yvbVALZ/Yvvv\nbS9eV+TLcM+BkfTyGtvatrzZYXv1uv9Ekv6wrgylvWdLenZZHpH0vyTtXWeGdWw/YPsBSR8bRPsT\nePcgi7yk3cvf4/k1t7urpK3KsqiuCX+kpP8jqZZziSS9el2GQRjKI3pJuwIfp/p4+jDVl6LbUvV3\nLbR9Vw0Zvkv1cfjrtu/pWL8F1UflBcAVts/td5bJSLrH9q41tHMMcBpVt8DmwFtsX1e21TLapbT1\n58BCqv3hVKpug5uo/h4ft/25GjKcPn4V1SiL8+CJ/uK+a0IOSV+zfXRZnke1j3wXOBj4WF3/NyTd\nBBxg+1FJpwJ7AF8DDgWwfVwNGf4T+A+qkXkXUl3jprY33aE8M5aqv/M0qmFiv4VqnCrweuAi4MAa\nMhwBHEf1Bc/uVG84v0P1Keky4DTbfb+KpaQlk22ivsslfwjYz/ZqSQcAX5D0Qdtfpd7L0b4N2Jvq\n73A38Bzba1RdTOoKoO+Fnqr77ntU+8C6f/t8oO9DfhuYY7eO5Q8Ah9q+s3QhLQXOrSnHZrYfLcsv\nA/Yvn7rPl/TDmjL8mOqN5XXAe4BzJH0VuNATzH3dc3V/IdKjLzZun8q2PubZHJjNBBML1ND2Q8BR\nVOP3O2+HAPfXlOHGcfdnUxWUk6jpy/HS7oqO5R+O21bXkMJnUB2E/BPw+2XdTwewXww8x7i/x7JB\n/D1KW5dSvclA9Sl8t7L8rPH7SR2vRbn/7PL/4yrg3n63P6xH9E25FjwAtv8LWF13u8XVwKOe4KhA\n0q01ZXhE0h62fwJVH305KeZrVEfYdbGkzcvf44kzlEvfaC3fR9l+BHinpP2AC8qJQrV/F9aQHC+S\n9AuqTxRbSppd9o0tqG+IJ1QjW86T9DdUJ1XeIOkGYDvg3TVleMonW1fDwU8HTpe028RP6WHj5d1l\nqKgB16OPJ0l6EdWbze3j1m8OHGP7gppy7Eo1bO6xcet3Ava0/Z06cnS0K+AvgYNsv6nOtpuYoyPP\ndlR/j6tqbndPqoshzqQ6a/k61zQ6TtIhtr9bR1sTtj+MhT6eVEb/rPePuDGPGfYMTcnRhAxNydGE\nDE3JMegMQz+8ch1JKwadYUCukPT2cjT7BElbSDpU0iKqLq22Z2hKjiZkaEqOJmRoSo6BZmjNEb2k\n623vM+gcdSv9z8cBbwTWjf7ZiqoP9DLgDPd59E8TMjQlxyQZOkdjDfK1qDVHE/4eTckx6AxtKvR/\nZ7uWS9E2VekTnwX8p+2Hp2uGpuRoQoam5GhChqbkGESGoSz0g+7viogYJsPaR9+EPreIiKEwrEf0\nA+9/jIgYFkNZ6Ds1oc8tIqLJhr7QR0TE+g1rH31ERGykFPqIiJZLoY/WkXS0JKuPE1xIGlV1nXMk\nzdXTr/8e0Rgp9NFGxwLfLz/7zvYy1zShSMRUpNBHq0jahmpGqeOpJtpA0maSzpD0Y0mXS/qmpNeV\nbftJ+p6k5ZIuVTWf6GS/ez9JP1Q1WcWJHesPkfSNsvxSSTeU2/WSnlHWf0DSjeX5p/TvFYh4umG9\nHn3EZOYB37Z9m6QHVF2PfXdgFNgL+D3gFuDzZWjup4F5tsckvQE4meocjYmcA7zN9pWSPjHJY94L\nnGj7B+VN51eSjiy5XuxqOrva5ziO6S2FPtrmWOBTZfmicn8m8KVy7fE1kq4o258HvAC4XNU87jOY\nZAIZVddQ3872lWXVF4AjJ3joD4BPSroA+IrtVZJeBpzjMp2d7Qe7/DdGbJIU+miNcqR8KPBCSaYq\n3Aa+OtlTgJW2D+pVBtunqJrN6ZXADyQd3qvfHTFV6aOPNnkd8AXbu9ketb0LcCfwIPDa0le/I9V8\nugC3AiOSDoLqLGtJE059WM66fljSH5VVb5zocaqmVLzR9qnAdcDzgcuBt0raujwmXTdRqxzRR5sc\nC5w6bt2XgT2ppo67mWqO4RXAz23/pnwpe7qkZ1L9fzgNWDnJ738rVd++qa6pNJF3Svpj4PHye75l\n+9eS/hseNmcEAAAAcElEQVSwTNJvgG8CH5rqPzJiU+USCDEtSNrG9i8lPQu4Fji4TNAc0Xo5oo/p\n4hvlC9UtgI+myMd0kiP6iHEkfQY4eNzqT9k+ZxB5IrqVQh8R0XIZdRMR0XIp9BERLZdCHxHRcin0\nEREtl0IfEdFy/x97/+V8xhq5ngAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18ef355470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_train.groupby('Age_disc')['Age'].count().plot.bar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The majority of people on the Titanic were between 16-40 years of age.\n",
    "\n",
    "Now, we can discretise Age in the test set, using the same interval boundaries that we calculated for the train set. See below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Age_disc_labels</th>\n",
       "      <th>Age_disc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>42.0</td>\n",
       "      <td>14.4583</td>\n",
       "      <td>0</td>\n",
       "      <td>Bin_6</td>\n",
       "      <td>(40.0, 48.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>648</th>\n",
       "      <td>18.0</td>\n",
       "      <td>7.5500</td>\n",
       "      <td>0</td>\n",
       "      <td>Bin_3</td>\n",
       "      <td>(16.0, 24.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>278</th>\n",
       "      <td>7.0</td>\n",
       "      <td>29.1250</td>\n",
       "      <td>0</td>\n",
       "      <td>Bin_1</td>\n",
       "      <td>(-0.001, 8.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>35.0</td>\n",
       "      <td>146.5208</td>\n",
       "      <td>1</td>\n",
       "      <td>Bin_5</td>\n",
       "      <td>(32.0, 40.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>255</th>\n",
       "      <td>29.0</td>\n",
       "      <td>15.2458</td>\n",
       "      <td>1</td>\n",
       "      <td>Bin_4</td>\n",
       "      <td>(24.0, 32.0]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Age      Fare  Survived Age_disc_labels       Age_disc\n",
       "495  42.0   14.4583         0           Bin_6   (40.0, 48.0]\n",
       "648  18.0    7.5500         0           Bin_3   (16.0, 24.0]\n",
       "278   7.0   29.1250         0           Bin_1  (-0.001, 8.0]\n",
       "31   35.0  146.5208         1           Bin_5   (32.0, 40.0]\n",
       "255  29.0   15.2458         1           Bin_4   (24.0, 32.0]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test['Age_disc_labels'] = pd.cut(x = X_test.Age, bins=intervals, labels=labels, include_lowest=True)\n",
    "X_test['Age_disc'] = pd.cut(x = X_test.Age, bins=intervals,  include_lowest=True)\n",
    "\n",
    "X_test.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x18ef5db0f0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HZv3XW8bx2Q5NPQBExNMRsSB/PV1OhAiyO+/g9bOKLRTXpHarpO9J+mtgpqTL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\ninHhNzOrGBd+M7OK+f/PLdv5VBpj3QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18ef5c1780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# if the distributions in train and test set are similar, we should expect similar distribution of \n",
    "# observations in the different intervals in the train and test set\n",
    "# let's see that below\n",
    "\n",
    "t1 = X_train.groupby(['Age_disc'])['Survived'].count() / np.float(len(X_train))\n",
    "t2 = X_test.groupby(['Age_disc'])['Survived'].count() / np.float(len(X_test))\n",
    "temp = pd.concat([t1,t2], axis=1)\n",
    "temp.columns = ['train', 'test']\n",
    "temp.plot.bar()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, the proportion of passengers within each bin is roughly the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x18ef6fa5c0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VPZwZY/swYuJi/vTuUj68rT8dG9d0uiyRUtmfnc+0hVuYvngbhw4XMCCmHv8a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\nD2diR2RoZz4b4rrP+KPOwPoyljtJH5T0xQjyndGchJWfLrYT2jHTxXY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      "text/plain": [
       "<matplotlib.figure.Figure at 0x18ef4dbf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# and now let's observe the relationship between age and surival again, using the discrete Age transformed \n",
    "# variable\n",
    "\n",
    "fig = plt.figure()\n",
    "fig = X_train.groupby(['Age_disc'])['Survived'].mean().plot(figsize=(12,6))\n",
    "fig.set_title('Normal relationship between variable and target')\n",
    "fig.set_ylabel('Survived')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x18ef779208>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YrgWeJKEc2iWb284ZzkerN/OzZz7CXTPWiIjIvlERLzGtsLiU5CTjxMFqpZHE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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18ef4b9278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "fig = X_train.groupby(['Age_disc'])['Survived'].count().plot(figsize=(12,6))\n",
    "fig.set_title('Number of passengers within each Age bin')\n",
    "fig.set_ylabel('No of Passengers')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, by dividing Age into bins, we removed some of the noise plotted in the previous graph (a few cells ago) using the untransformed Age. Using the discrete variable Age, we observe as expected that children (<16) had the highest survival chance.\n",
    "\n",
    "What happens to older people is less clear from the discrete variable. It looks like people between 32-40 and 48-56 are more likely to survive, than people from 40-48. This might or might not be true and more research would be needed to determine if this was the case, what the reason behind it was. In addition, it looks like being extremely old, was very favourable for survival (look at the 72-80 bucket). However, most likely, these are consequences of an arbitrary binning strategy. There are very few people in the bucket 72-80, and thus, the fact that 1 of them survived inflates (overestimates) the survival rate for that bucket. And the same is true for the remaining of the bins, the lowest the amount of observations within buckets, the highest the risk of over or underestimating the target (survival in this case). So we begin to see some of the consequences of this binning strategy.\n",
    "\n",
    "Similarly to what we did with the equal frequency discretised Age variable in the previous lecture, here as well to squeeze a bit more performance out of the machine learning algorithm, we can add a layer of transformation by sorting the bins using the survival rate (the caveat being that the survival rate may be over or underestimated as we explained in the previous paragraph). But just for a demonstration, let's go ahead. See below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Combine discretisation with label ordering according to target\n",
    "\n",
    "You can revise the lectures on engineering categorical variables to re-cap on how to preprocess labels.\n",
    "\n",
    "For this demonstration I will assign ordinal numbers to the different bins, according to the survival rate per bin."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# order the bins according to survival rate\n",
    "ordered_labels = X_train.groupby(['Age_disc_labels'])['Survived'].mean().sort_values().index\n",
    "ordinal_label = {k:i for i, k in enumerate(ordered_labels, 0)}\n",
    "\n",
    "# transformed the discrete age variable\n",
    "X_train['Age_disc_ordered'] = X_train.Age_disc_labels.map(ordinal_label)\n",
    "X_test['Age_disc_ordered'] = X_test.Age_disc_labels.map(ordinal_label)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x18ef32d198>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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g1BG9+O5Zw5k0sg/9unWIOkwRSXEJJQ0zOwq4F+jr7sea2ViCdo7/Smp0csj2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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18ef7beeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "fig = X_train.groupby(['Age_disc_ordered'])['Survived'].mean().plot()\n",
    "fig.set_title('Monotonic relationship between discretised Age and target')\n",
    "fig.set_ylabel('Survived')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Fare\n",
    "\n",
    "Let's look at the consequences of equal width discretisation on highly skewed variables like Fare."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x18ef85b748>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NzMwMPIcHHt7D/Yfe+A/5Hr9z5g0/59zcHMO8V8vJJNUKk1XvJNUK46930LtuTiVZBdA9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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18ef4e1ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's plot the hist, to remind us of the skewness of Fare\n",
    "\n",
    "X_train.Fare.hist(bins=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "512.32920000000001"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fare_range = X_train.Fare.max() - X_train.Fare.min()\n",
    "Fare_range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 51, 102, 153, 204, 255, 306, 357, 408, 459, 510, 561]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min_value = int(np.floor(X_train.Fare.min()))\n",
    "max_value = int(np.ceil(X_train.Fare.max()))\n",
    "inter_value = int(np.round(Fare_range/10))\n",
    "\n",
    "intervals = [i for i in range(min_value, max_value+inter_value, inter_value)]\n",
    "intervals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(intervals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x18efa96ba8>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x18ef5c1390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_train['Fare_disc'] = pd.cut(x = X_train.Fare, bins=intervals, include_lowest=True)\n",
    "X_test['Fare_disc'] = pd.cut(x = X_test.Fare, bins=intervals, include_lowest=True)\n",
    "\n",
    "# if the distributions in train and test set are similar, we should expect similar distribution of \n",
    "# observations in the different intervals in the train and test set\n",
    "t1 = X_train.groupby(['Fare_disc'])['Survived'].count() / np.float(len(X_train))\n",
    "t2 = X_test.groupby(['Fare_disc'])['Survived'].count() / np.float(len(X_test))\n",
    "temp = pd.concat([t1,t2], axis=1)\n",
    "temp.columns = ['train', 'test']\n",
    "temp.plot.bar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For very skewed variables, discretisation using range is not a good option, as it ends up putting the majority of the observations within 1 or 2 buckets, and the remaining are almost empty or empty.\n",
    "\n",
    "For very skewed variables, quantile discretisation may be a better choice."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**That is all for this demonstration. I hope you enjoyed the notebook, and see you in the next one.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  },
  "toc": {
   "nav_menu": {
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